Log24

Saturday, March 5, 2011

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Filed under: General,Geometry — m759 @ 9:00 PM

A search for some background on Dmitri Tymoczko, the subject of yesterday's evening entry on music theory, shows that his name and mine once both appeared in the same web page— "This Week's Finds in Mathematical Physics (Week 234)," by John Baez, June 12, 2006 (linked to by the Wikipedia article on transformational music theory).

In that page, Baez speculates on the possibility of a connection between music theory and Mathieu groups and says—

"For a pretty explanation of M24, also try this:

Steven H. Cullinane, Geometry of the 4 × 4 square, http://finitegeometry.org/sc/16/geometry.html."

I know of no connection* between the groups I discussed there and music theory. For some background on Tymoczko's work, see the helpful survey "Exploring Musical Space," by Julian Hook (Science  magazine, 7 July 2006).

* Apart, that is, from the tesseract (see Geometry of the 4 × 4 Square) shown by Tymoczko in a 2010 lecture

http://www.log24.com/log/pix11/110305-TymoczkoTesseract.jpg

This is perhaps "Chopin's tesseract" from section 8.5 of Tymoczko's new book
A Geometry of Music  (Oxford University Press, 2011).

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